FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 2, PAGES 411-416

On singularity of solution to inverse problems of spectral analysis expressed with equations of mathematical physics

V. V. Dubrovsky
L. V. Smirnova

Abstract

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The inverse problem for the Laplacian under the Robin's boundary conditions is considered. We prove the following

Theorem. If $q$_p, $p=1,2$, are real twice continuously differentiable functions on $\$\; \backslash bar\; \{\backslash Omega\; \}\; \$$ and there exists a subsequence $i$_k of positive integers such that $||\; v$_ik(q_p) ||_L2(S) £ const |l_ik| ^b, where $v$_i(q_p) are orthonormal eigenfunctions of the operator $-$D +q in the case of Robin's boundary conditions with the eigenvalues $$l _i, $i$Î N, and $0$£ b < 4^-1 then there exists an infinite subsequence $i$_klm of positive integers such that the conditions

imply $q$₁=q₂.

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Last modified: July 6, 1999